Simplify the following expression: $ x = \dfrac{r + 7}{8r + 3} - 5 $
Explanation: In order to add expressions, they must have a common denominator. Multiply the second expression by $\dfrac{8r + 3}{8r + 3}$ $ \dfrac{-5}{1} \times \dfrac{8r + 3}{8r + 3} = \dfrac{-40r - 15}{8r + 3} $ Therefore $ x = \dfrac{r + 7}{8r + 3} + \dfrac{-40r - 15}{8r + 3} $ Now the expressions have the same denominator we can simply add the numerators: $x = \dfrac{r + 7 - 40r - 15}{8r + 3} $ $x = \dfrac{-39r - 8}{8r + 3}$